Partha earns 15 per cent on an investment but loses 10 per cent. on another investment. If the ra tio of two investments is 3:5, then the combined loss per cent is

Options

A. `5/4` %
B. `4/5` %
C. `8/5` %
D. `-5/8` %

Answer

To find the combined loss percentage when Partha earns 15% on one investment and loses 10% on another investment with a ratio of 3:5, we can follow these steps:

### Step 1: Assign values to the investments
Let the first investment (which earns 15%) be represented as \(3x\) and the second investment (which loses 10%) be represented as \(5x\).

### Step 2: Calculate the profit from the first investment
The profit from the first investment can be calculated as:
\[ \text{Profit} = \text{Investment} \times \text{Profit Percentage} = 3x \times \frac{15}{100} = \frac{45x}{100} = 0.45x \]

### Step 3: Calculate the loss from the second investment
The loss from the second investment can be calculated as:
\[ \text{Loss} = \text{Investment} \times \text{Loss Percentage} = 5x \times \frac{10}{100} = \frac{50x}{100} = 0.5x \]

### Step 4: Calculate the total investment
The total investment is:
\[ \text{Total Investment} = 3x + 5x = 8x \]

### Step 5: Calculate the total profit and loss
Now, we can find the total profit and loss:
\[ \text{Total Profit} = 0.45x \]
\[ \text{Total Loss} = 0.5x \]

### Step 6: Calculate the net result
The net result can be calculated as:
\[ \text{Net Result} = \text{Total Profit} - \text{Total Loss} = 0.45x - 0.5x = -0.05x \]
This indicates a loss.

### Step 7: Calculate the combined loss
The total loss in terms of percentage can be calculated as:
\[ \text{Loss Percentage} = \left( \frac{\text{Net Loss}}{\text{Total Investment}} \right) \times 100 = \left( \frac{0.05x}{8x} \right) \times 100 = \left( \frac{0.05}{8} \right) \times 100 = 0.625\% \]

### Step 8: Present the final answer
Since we are looking for the combined loss percentage, we can express it as:
\[ \text{Combined Loss Percentage} = 0.625\% \]

Thus, the combined loss percentage is approximately **0.625%**.

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